Measurement method to facilitate production of self-aligning laser gyroscope block

ABSTRACT

A method for locating the position for a concave mirror alignment device on a RLG block, comprising the following steps: 1) mount a “log” onto a CNC machine, 2) select several points along the length of the log for measurement; 3) measure the mirror mounting surface radial distances at each of the several points from the “front” of the log; 4) measure the surface radial distances at each of the several points from the “rear” of the log; 5) determine the radius, and ultimately the diameter, of a circle tangent to the mirror mounting sides of the log, for each of the several selected points; 6) determine a “best fit” equation to describe the diameters as a function of position along the log; 7) determine the offset along the x axis for the mirror mounting device of each block within the log.

CROSS-REFERENCE TO RELATED APPLICATION(S)

None.

BACKGROUND OF THE INVENTION

The present invention is a measurement method to facilitate theproduction of self-aligning laser gyroscope blocks.

One embodiment of this invention is application to a ring lasergyroscope (RLG). A RLG is commonly used to measure the angular rotationof a vehicle, such as an aircraft. Such a gyroscope has twocounter-rotating laser light beams which move within a closed loop pathor “ring” with the aid of successive reflections from multiple mirrors.The closed path is defined by an optical cavity which is interior to astructural gyroscope frame or “block”. In one type of RLG, the blockincludes planar top and bottom surfaces that are bordered by six planarsides that form a hexagon-shaped perimeter. Surfaces on each of thesides define mounting areas for components such as mirrors andelectrodes. For example, three planar non-adjacent sides of the blockform the mirror mounting surfaces for three mirrors at the corners ofthe optical path, which is triangular in shape.

Operationally, upon rotation of the RLG about its input axis (which isperpendicular to and at the center of the planar top and bottom surfacesof the block), the effective path length of each counter-rotating laserlight beam changes, and a frequency differential is produced between thebeams that is nominally proportional to angular rate. This differentialis then measured by signal processing electronics to determine theangular rotation of the vehicle.

A typical RLG block has three electrodes, which are disposed one on eachof three non-adjacent planar side surfaces, and three mirrors, one ofwhich has a concave reflective surface while the other two mirrors haveplanar reflective surfaces. The curved mirror serves two main purposes.First, the curvature of the reflective surface controls the diameter andthe primary mode of the counter-rotating laser light beams. Second, thecurvature of the reflective surface is used to align thecounter-rotating laser light beams within the optical cavity so that thelight beams are at substantially maximum intensity to minimize RLG biaserrors. In particular, this latter purpose is accomplished due to theinherent attributes of the concave reflective surface. By nature, theangle of the surface of a concave mirror varies in accordance with itscurvature. Therefore, an incident laser light beam can be redirected or“steered” by translating (i.e., moving) the curved mirror within theplane of its respective block mounting surface.

In practice, with the two planar mirrors already mounted on the block,the concave mirror is translated to selectively steer the light beamwithin the optical cavity via a conventional mirror movement mechanism.During translation of the concave mirror, a detector, such as aphotodiode, senses the intensity of the laser light out put from thecavity through one of the planar mirrors that is partially transmissive.The photodiode generates an electrical signal representative of theintensity of the laser light output from the optical cavity. This signalis monitored by a voltmeter during such translations of the concavemirror until a mirror position is found exhibiting a maximum output onthe voltmeter. This mirror position indicates that the counter-rotatinglaser light beams are at substantially maximum intensity and thereforeare optimally aligned within the aperture of the optical cavity. Theconcave mirror is then secured to its mounting surface on the block atthe optimum mirror position to complete the laser light beam alignmentprocess.

Though the above described alignment mechanism and process adequatelyaligns the counter-rotating laser light beams within the optical cavityof the block so as to minimize RLG bias errors, there is at least onedisadvantage. The mechanism and process described requires a great dealof handling of the concave mirror, particularly when translating themirror about its mounting surface to identify the mirror's optimummirror mounting position. The greater the extent of concave mirrormanipulation, the better the chance of introducing contaminants (i.e.,dirt) to or damaging the delicate reflective surface of the mirror. Anydamage and/or contamination increases the likelihood of bias errors anddegrades RLG performance. If the bias errors are too great and/or theRLG performance too corrupted, the RLG must be rebuilt or scraped. Thisincreases the manufacturing cost of producing the RLG's.

There is a need for improved device and method for achieving opticalalignment of an optical cavity such as the optical cavity of an RING. Inparticular, there is a need for a mirror alignment device and methodthat reduces the amount of mirror handling needed to align the lightbeams within the optical cavity. In addition, the device and methodshould reduce the likelihood of mirror reflective surface damage and/orcontamination during alignment, to reduce the number of RLG's needing tobe rebuilt or scrapped. Moreover, the mirror alignment device and methodshould be relatively easy and inexpensive to practice and shouldfacilitate automation of assembly.

BRIEF SUMMARY OF THE INVENTION

The present invention is a method for locating the optimal position fora concave mirror alignment device on a RLG block so as to minimize RLGbias errors. A preferred embodiment of method includes the followingsteps: 1) mount a “log” onto a CNC machine; 2) select several pointsalong the length of the log for measurement; 3) measure the mirrormounting surface radial distances at each of the several points from the“front” of the log; 4) measure the surface radial distances at each ofthe several points from the “rear” of the log; 5) determine the radius,and ultimately the diameter, of a circle tangent to the mirror mountingsides of the log, for each of the several selected points; 6) determinea “best fit” equation to describe the diameters as a function ofposition along the log; 7) determine the offset along the x axis for themirror mounting device of each block within the log.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view of a RLG log.

FIG. 2 is a plan view of a RLG log, with the measurement pointsindicated for a preferred embodiment.

FIG. 3 is a diagram illustrating the measurement method of the presentinvention.

FIG. 4 is a diagram illustrating the difference in elevation of theopposite ends of a log in a V-block measurement.

FIG. 5 is a perspective view of a RLG block showing a mirror mountingdevice.

DETAILED DESCRIPTION

FIG. 1 shows a ring laser gyroscope (RLG) log 10. Log 10 is formed of aglass, glass ceramic, or like material. Suitable log materials includethe glass ceramic material marketed under the trademarks “Cervit” and“Zerodur”. An example of a suitable glass material is a borosilicateglass marketed under the trademark “BK-7”.

The cross section of log 10 is generally triangular shaped with ahexagonal outer periphery. The hexagonal outer periphery includes threeplanar non-adjacent sides that form first, second and third mirrormounting surfaces A, B and C, and three further planar non-adjacentsides F, G and H.

To form individual RLG's, log 10 is drilled, or machined, with variousinternal passages and bores and then sliced into individual blocks 12.However, before such machining is accomplished, the measurement methodof the present invention is employed to determine the optimal locationfor machining a mirror mounting device for a concave mirror. Such amirror mounting device is disclosed in U.S. Pat. No. 5,960,025, toThorland et al., which is fully incorporated herein.

When log 10 is to be machined, it is mounted on supports so thatmachining operations can be accomplished by a computer-controlledmachining device. One such device is known as a CNC (computer numericalcontrol) machine. However, the turning axis of the supports does notusually coincide exactly with the true center of log 10. The method ofthe present invention accurately positions a concave mirror mountingdevice despite that discrepancy and compensates for any taper orcurvature of the log.

In a preferred embodiment, after log 10 is mounted on the CNC machine,several points along the x axis are selected as measurement points. Themore points are selected, the more accurate the resulting offsetdeterminations will be for each block 12. In a preferred embodiment, asshown in FIG. 2, twelve blocks will be cut from each log 10, and 13points along the x axis of log 10 are selected for measurement.

FIG. 3 is a diagram illustrating a preferred embodiment of the method ofthe present invention. As can be seen in FIG. 3, the turning axis of thesupports 14 does not coincide with the true center 16 of log 10. Center16 is defined as the center of the circle 1 8 which is tangent to mirrormounting surfaces A, B and C. Measurement “a” is the distance from axis14 to side “A.” Measurement “b” is the distance from axis 14 to side“B.” Measurement “c” is the distance from axis 14 to side “C.”

In a preferred embodiment, the coordinate system originates at center16. The x axis, shown in FIG. 1., runs through center 16 along thelength of log 10. The Y & Z axes, shown in FIG. 3, exist in a planeperpendicular to the x axis. The Z axis is perpendicular to side A. TheY axis is parallel to side A and perpendicular to the Z axis. The U axisis defined by the numerical control system of the CNC machine and isindependent of the X-Y-Z coordinate system. The relationship between thepoints on the U axis is as follows: U_(c)=(U₁+U₂)/2.

For each chosen position along the x axis, surface radial distances a, band c are measured from the “front” of log 10, as shown in the topportion of FIG. 3. Then, log 10 is rotated 180 degrees. Surface radialdistances a, b and c are then measured from the “rear” of log 10, asshown in the bottom portion of FIG. 3. The “front” and “rear” numericalvalues on the U axis are used to calculate the distances a, b & c. Forexample, as shown in FIG. 3, a=(U₂−U₁)/2.

Let “j” be the angle formed by the intersection of the planes defined bysurfaces A and B. Let “k” be the angle formed by the intersection of theplanes defined by sides A and C. Let R be the radius of circle 18. Let(Y, Z) be the coordinates of turning axis 14 relative to center 16.Then,

R=[a*sin k]+[b*sin j]+[c*sin (j+k)]sin k+sin j+sin (j+k)

In the simple case where j=k=60 degrees, the following relations result:

R=(a+b+c)/3

Y=(b−a)/sqrt(3)

Z=(a+b−2c)/3

R is calculated for each of the points selected along the length of thelog (the x axis).

The radius (R) measurements taken above are doubled to find the diameter(D) of circle 18 at each selected point x along the length of the log.The resulting data is then used to determine a best-fit curve todescribe the diameters as a function of position along the log. Anynumerical analysis method may be used, but in a preferred embodiment, asecond-order quadratic equation is used. Taking a derivative of thisfunction, the slope can be determined, which describes the net taper orcurvature of the three surfaces A, B & C to which the mirrors will laterbe mounted.

The quadratic equation of a preferred embodiment takes the followingform:

 D(x)=D₀+1.5*(αx+βx²)

FIG. 4 explains how the factor of 1.5 is derived. Log 10 is placed inV-block 20, which has an apex angle 22 of 60 degrees, so that two of themirror mounting sides A, B, or C rest on the planar surfaces of V-block20. Circle 18 presents the circle which is tangent to sides A, B, and Cat or near one end of log 10. Circle 18′ presents the circle which istangent to sides A, B, and C at or near the opposite end of log 10. Thedifference in the elevation of the opposite ends of log 10 in V-block 20indicates the taper of the log, which affects the ultimate offset neededfor a mirror mounting device for each block 12 that will be cut from log10.

Radius R of circle 18 forms one side of a right triangle, where theangle opposite R is 30 degrees. By trigonometric functions, thehypotenuse of the right triangle is 2R. Twice the radius of circle 18,or 2R, equals D, the diameter of circle 18: 2R=D. Similarly, radius R′of circle 18′ forms one side of a right triangle, where the angleopposite R′ is 30 degrees. By trigonometric functions, the hypotenuse ofthe right triangle is 2R′. Twice the radius of circle 18′, or 2R′,equals D′, the diameter of circle 18′:2R′=D′.

The distance from the top of circle 18 to apex 22 is 3R because it isthe distance of hypotenuse 2R plus one radius. By simple multiplicationof both sides of the 2R=D equation, 3R=1.5D. Similarly, the distancefrom the top of circle 18′ to apex 22 is 3R′ because it is the distanceof hypotenuse 2R′ plus one radius. By simple multiplication of bothsides of the 2R′=D′ equation, 3R′=1.5D′. By subtraction, the differencein the elevation of the opposite ends log 10 in V-block 20 is1.5D′−1.5D=1.5 (D′−D). Thus, the block dimension relating to a V-blockmeasurement of pyramidal angle is 1.5 times the diameter difference.

The α and β values of the quadratic equation are then used to calculatethe appropriate offset for the mirror mounting device on ablock-by-block basis along the log. The equation for the offset at eachpoint x along the log follows:

 offset(x)=−1,500*r*(α+2βx)

where

offset(x) is in units of mils;

r is the radius of curvature (in inches) of a concave reflective surfaceof the curved mirror; in a preferred embodiment, r=9.5 inches;

x is the distance of the selected point from the end of the log (ininches); and

−1,500 comes from multiplying 1.5 by −1000. The factor of 1000 convertsthe units from inches to mils, and the negative sign indicates that thedirection of the offset is opposite the direction of the slope of themirror mounting surface (the mirror is shifted “downhill”).

Once the offset for each block is calculated, the mirror mounting devicefor the concave mirror for that block can be machined into the block atthe proper location.

FIG. 5 is a perspective view of a RLG block showing a mirror mountingdevice. Mirror mounting device 24 is offset along the x axis (either inthe positive or negative direction indicated by arrow 32) relative tothe centerline S—S of the optical cavity of each block 12. Mirrormounting device 24 comprises recessed moat 26 machined into mirrormounting surface A. Such machining results in ring 28, formed interiorto moat 26. The interior edge of ring 28 is defined by well 30 into theinterior of block 10. The exterior edge of ring 28 is defined by theinterior edge of moat 26. The face surface of ring 28 is co-planar withthe surfaces of planar side A. In comparison, the surface of moat 26 isbelow the surfaces of ring 28 and side A. The exterior edge of ring 28defines mirror alignment device 24, and it is on this edge that theconcave reflective surface of the curved mirror rests. In accordancewith the present invention, because of the offset of moat 26, andtherefore the offset of mirror mounting edge 24, ring 28 may not beuniform in width along its circumference.

One advantage of the present invention is that it allows the entireprocess to be accomplished by one machine. Because many CNC machineshave precision measurement capabilities, the entire process:measurement, fitting of the quadratic equation, calculation of theoffsets, and machining of the log, is achieved under CNC computercontrol. This scheme avoids issues of confusion over communication ofmeasurement results between different machines or operators.

The process is also capable of positioning the mirror mounting device tocompensate for any irregularities in the log, such as linear taper orcurvature of the log, or tilt of the critical mirror mounting surfaces.This allows the CNC machine to position the mirror mounting device on ablock-by-block basis within the log, thereby increasing the accuracy ofmachining for each RLG. The invention leads to significant economicsavings because fewer parts will need to be rejected because of suchirregularities.

Although the present invention has been described with reference topreferred embodiments, workers skilled in the art will recognize thatchanges may be made in form and detail without departing from the spiritand scope of the invention.

What is claimed is:
 1. A method for positioning a mirror mounting deviceon a ring laser gyroscope structure, the structure comprising a loghaving a plurality of mirror mounting side surfaces, the methodcomprising the steps of: selecting a plurality of measurement pointsalong the length of a log; determining a diameter of a circle tangent tothe mirror mounting surfaces of the log at each of the selected points;determining a best-fit curve to describe the diameter measurements as afunction of position along the length of the log; calculating where toposition the mirror mounting device relative to a center of an opticalcavity of a block of the log, from the best-fit curve; and machining themirror mounting device onto the ring laser gyroscope structure.
 2. Themethod of claim 1 wherein 13 measurement points are selected along thelength of the log.
 3. The method of claim 1 wherein the log has a threemirror mounting side surfaces and wherein the angle between each pair ofconsecutive mirror mounting side surfaces is 60 degrees.
 4. The methodof claim 3 wherein determining the diameter of a circle tangent to themirror mounting surfaces of the log at a point comprises: measuring theradial distance between a turning axis of the log and each mirrormounting surface; averaging the radial distances to find the radius ofthe circle; and doubling the radius to find the diameter of the circle.5. The method of claim 3 wherein the best-fit curve is described by theequation: D(x)=D₀+1.5*(αx+βx²) where D(x) is a diameter of the circle atposition x along the log, and D₀ is a diameter of the circle atsubstantially one end of the log.
 6. The method of claim 5 wherein theposition of the mirror mounting device relative to a center of anoptical cavity of a block of the log is described by the equation:offset(x)=−1,500*r*(α+2βx) where offset(x) is the offset distance of themirror mounting device relative to a center of an optical cavity of ablock of the log at position x along the log, in units of mils; and r isthe radius of curvature of a concave surface of a mirror, in units ofinches.